Math Help - Partial Derivatives

1. Partial Derivatives

I can't solve this for the life of me, so I'm appealing to the Math Help Forum! Here's the question:

Let f(x) and g(y) be two differentiable functions and h(x,y)=f(x)+g(y) be with hx=sin(x) and hy=cos(x), and h(π/2,π/2)=5. Find h(x,y).

I have tried and tried, but I can't seem to solve it. I know that the partial w.r.t. y of y*cos(x) will give cos(x), but what do you add to get the partial w.r.t. x to get sin(x) as well? And what about that
h(π/2,π/2)=5 part? HELP!

2. No such function exists since h = f(x) + g(y)

hy = g ' (y) = cos(x) is a contradiction

since g depends only on y.

3. I know... I thought I was missing something, but I'm convinced now that it must be a typo on my homework... it has to be cos(y), NOT cos(x)...

4. I assume you'll have no pblm now but just in case:

h(x,y) = -cos(x) + sin(y) + C

h(pi/2,pi/2) = 1+ C = 5

C = 4

h(x,y) = -cos(x) + sin(y) + 4

5. Hadn't got that far yet, but thanks!